The first step in the generation of the resource states is to create one-dimensional hybrid cluster states that extend in the temporal direction.
Recall from sec:encodedqubits,sec:canCVCS that both GKP qubit cluster states and CV cluster states require \(CZ=e^{i \hat{q}\otimes \hat{q}}\)  gates.
Given a single physical \(CZ\)  gate (implemented via beam-splitters and squeezers as shown in fig:Gaussgates), a linear cluster state can be generated in the time domain using optical delay lines [1]}, [2]}, [3]}.
Fig:CZa depicts the setup for the generation of this 1D cluster state.
The circuit receives as input the states generated using GBS state preparation.
The first mode is swapped into the optical delay line, whose length is set equal to the distance between subsequent optical pulses.
This mode returns to the interferometer and interacts with the next mode at the \(CZ\)  gate.
At the final step of operation, the cycling light is kicked out of the delay line by the same physical swap gate.
This interaction repeats for each of the incoming modes.
In this way, a one-dimensional cluster state is generated.
